The Saurashtra people have a very unsettled past. They lived in Gujarat, but then Gazni Mohammed invaded around 1000 AD and the Saurashtras took off for Devagiri, farther south. They stayed there for two centuries, but then that empire collapsed and they were on the move again, even farther south to another kingdom. They were traditionally weavers, and frequently were royal weavers, enjoying the patronage of the local king.
Perhaps their being a perpetual minority for the past thousand years (and living by the grace of the local king for hundreds of years of that) contributed to them not sticking fiercely to their own language and/or script. Indeed, my sources don’t cite any material in the Saurashtra script before the late 1800s, when Medhavi Sri T.M. Rama Rai set up a press in Saurashtra script. In 1920 AD, however, a resolution was passed declaring that Saurashtra should be written with the Devanagari script. In practice, however, the language is now mostly written in a modified version of Tamil script.
The Saurashtra script is a pretty generic Brahmi-derived script, with one exception: it has a diacritic for consonants, turning e.g. “ma” and “ra” into “mha” and “rha”.